Submission #1344637

#TimeUsernameProblemLanguageResultExecution timeMemory
1344637avighnaEvent Hopping 2 (JOI21_event2)C++20
100 / 100
466 ms30752 KiB
#include <bits/stdc++.h>

using namespace std;

struct interval {
  int l, r;
  int i;
  auto operator<=>(const interval &r) const = default;
};

class lazy_segment_tree {
  int n;
  vector<int> seg, lazy;

public:
  lazy_segment_tree(int n) : n(n), seg(4 * n), lazy(8 * n) {}

  void push(int v, int tl, int tr) {
    seg[v] += lazy[v] * (tr - tl + 1);
    lazy[2 * v] += lazy[v];
    lazy[2 * v + 1] += lazy[v];
    lazy[v] = 0;
  }

  void apply(int v, int tl, int tr, int l, int r, int x) {
    push(v, tl, tr);
    if (tr < l || r < tl) {
      return;
    }
    if (l <= tl && tr <= r) {
      lazy[v] += x;
      push(v, tl, tr);
      return;
    }
    int tm = (tl + tr) / 2;
    apply(2 * v, tl, tm, l, r, x);
    apply(2 * v + 1, tm + 1, tr, l, r, x);
    seg[v] = seg[2 * v] + seg[2 * v + 1];
  }
  void apply(int l, int r, int x) { apply(1, 0, n - 1, l, r, x); }

  int query(int v, int tl, int tr, int l, int r) {
    push(v, tl, tr);
    if (tr < l || r < tl) {
      return 0;
    }
    if (l <= tl && tr <= r) {
      return seg[v];
    }
    int tm = (tl + tr) / 2;
    return query(2 * v, tl, tm, l, r) + query(2 * v + 1, tm + 1, tr, l, r);
  }
  int query(int l, int r) { return query(1, 0, n - 1, l, r); }
};

const int inf = 1e9;

class segment_tree {
  int n;
  vector<int> seg;

public:
  segment_tree(int n) : n(n), seg(2 * n, -inf) {}

  void set(int i, int x) {
    for (seg[i += n] = x, i >>= 1; i > 0; i >>= 1) {
      seg[i] = max(seg[2 * i], seg[2 * i + 1]);
    }
  }
  void apply(int i, int x) {
    i += n;
    for (seg[i] = max(seg[i], x), i >>= 1; i > 0; i >>= 1) {
      seg[i] = max(seg[2 * i], seg[2 * i + 1]);
    }
  }

  int query(int l, int r) {
    int ans = -inf;
    for (l += n, r += n + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1)
        ans = max(ans, seg[l++]);
      if (r & 1)
        ans = max(ans, seg[--r]);
    }
    return ans;
  }
};

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);

  int n, k;
  cin >> n >> k;
  vector<interval> a(n);
  vector<int> buff;
  for (int i = 0, l, r; i < n; ++i) {
    cin >> l >> r;
    a[i] = {l, r, i};
    buff.push_back(l), buff.push_back(r);
  }
  auto A = a;
  sort(a.begin(), a.end(), [](interval a, interval b) { return a.r < b.r; });

  // for a given interval [l, r], find an interval ahead of it [l', r'] such that l' >= r
  segment_tree st(n);
  for (int i = 0; i < n; ++i) {
    st.set(i, a[i].l);
  }
  vector lift(n + 1, vector<int>(20));
  for (int i = 0; i < n; ++i) {
    int j = *ranges::partition_point(views::iota(i + 1, n), [&](int j) {
      return st.query(i + 1, j) < a[i].r;
    });
    lift[i][0] = j;
  }
  lift[n][0] = n;
  for (int bt = 1; bt < 20; ++bt) {
    for (int i = 0; i <= n; ++i) {
      lift[i][bt] = lift[lift[i][bt - 1]][bt - 1];
    }
  }

  sort(buff.begin(), buff.end());
  buff.erase(unique(buff.begin(), buff.end()), buff.end());
  auto comp = [&](int i) { return lower_bound(buff.begin(), buff.end(), i) - buff.begin(); };

  auto solve = [&](int L, int R) {
    // find first interval in a with their l >= L
    int i = *ranges::partition_point(views::iota(0, n), [&](int i) {
      return st.query(0, i) < L;
    });
    if (i == n || a[i].r > R) {
      return 0;
    }
    int k = 0;
    for (int bt = 19; bt >= 0; --bt) {
      if (lift[i][bt] != n && a[lift[i][bt]].r <= R) {
        k |= 1 << bt;
        i = lift[i][bt];
      }
    }
    return k + 1;
  };

  int cur = solve(1, int(1e9));
  if (k > cur) {
    cout << "-1\n";
    return 0;
  }

  set<pair<int, int>> curs;
  lazy_segment_tree lst(buff.size());
  vector<int> ans;
  for (int i = 0; i < n; ++i) {
    pair<int, int> _p = {A[i].l, int(1e9) + 1};
    auto itt = curs.upper_bound(_p);
    if (itt != curs.begin()) {
      itt--;
      // find an inteval with l <= our l
      if (A[i].r <= itt->second) { // full intersection
        continue;
      }
    }
    pair<int, int> p = {A[i].l, A[i].r};
    int q1 = lst.query(comp(A[i].l), comp(A[i].r));
    int q2 = lst.query(comp(A[i].l), comp(A[i].l));
    int q3 = lst.query(comp(A[i].r), comp(A[i].r));
    if (q1 - q2 - q3 != 0 || q2 > 1 || q3 > 1) {
      continue;
    }
    curs.insert(p);
    auto it = curs.find(p);
    int lef = 1, rig = 1e9;
    if (it != curs.begin()) {
      lef = prev(it)->second;
    }
    if (it != --curs.end()) {
      rig = next(it)->first;
    }
    int pcur = cur;
    cur -= solve(lef, rig);
    cur += solve(lef, p.first) + 1 + solve(p.second, rig);
    if (cur < k) {
      curs.erase(it);
      cur = pcur;
    } else {
      ans.push_back(i + 1);
      lst.apply(comp(p.first), comp(p.second), 1);
    }
  }

  for (int i = 0; i < k; ++i) {
    cout << ans[i] << '\n';
  }
}
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